lecture 04: fri 23 jan - louisiana state university

Physics 2102 Lecture 04: FRI 23 JAN

Electric Charge I

Physics 2113 Jonathan Dowling

Charles-Augustin de Coulomb (1736–1806)

Version: 12/26/14

Benjamin Franklin (1705–1790)

Let’s Get Started! Electric Charges…

•  Two Types of Charges: Positive/Negative •  Like Charges Repel •  Opposite Charges Attract

Atomic Structure: •  Negative Electron Cloud •  Nucleus of Positive Protons, Uncharged Neutrons The Unit of Electric Charge is the “Coulomb” which is “C”. Proton Charge: e = 1.60 × 10–19 C

Benjamin Franklin (1705–1790)

Rules of Electric Attraction and Repulsion Discovered by Benjamin Franklin:

Electrical Insulators

Benjamin Franklin (1705–1790)

Rules of Electric Attraction and Repulsion Discovered by Benjamin Franklin:

Electric Conductors

Benjamin Franklin (1705–1790)

Rules of Electric Attraction and Repulsion: ICPP

C and D attract B and D attract

−( )

−( )+( )

+( )+( )

+−

+− +( )

+( )+( )

12F1q+ 21F 2q−

12F 1q+ 21F2q+

12F 1q− 21F2q−

Force Between Pairs of Point Charges: Coulomb’s Law

Coulomb’s Law — the Force Between Point Charges: •  Lies Along the Line Connecting the Charges. •  Is Proportional to the Product of the Magnitudes. •  Is Inversely Proportional to the Distance Squared. •  Note That Newton’s Third Law Says |F12| = |F21|!!

Charles-Augustin De Coulomb (1736–1806)

12F1q+ 21F 2q−

12F 1q+ 21F2q+

12F 1q− 21F2q−

Force Between Pairs of Point Charges: ICPP

!Fpe(a)

!Fpe +

!Fee(c)

!Fpp(b)

2q−12F1q+ 21F

12r

Coulomb’s Law

�

F12 =k q1 q2

r122

�

k = 14πε0

with ε0 = 8.85 ×10−12 C2

Nm2

k = 8.99 ×109 Nm2

C2 ∝ kg m3

s2 C2

The “k” is the electric constant of proportionality.

Usually, we write:

Units: F = [N] = [Newton]; r = [m] = [meter]; q = [C] = [Coulomb]

Coulomb’s Law: ICCP

(a)  a > c > b (b)  less

!Fnet

!Fnet

!Fnet

Coulomb’s Torsion Balance Experiment For Electric Force Identical to Cavendish’s Experiment For

Gravitational Force!

k = 8.99 ×109 Nm2

C2 ∝ kg m3

s2 C2

The experiment measures “k” the electric constant of proportionality and confirms inverse square law.

�

F12 =k q1 q2

r122

http://www.dnatube.com/video/11874/Application-Of-Coulombs-Torsion-Balance

Two Inverse Square Laws

Newton’s Law of Gravitational Force Coulomb’s Law of

Electrical Force

Area of Sphere = 4πr2

Number of Lines of Force is Constant. Hence #Force Lines Per-Unit-Area is Proportional to 1/r2

Superposition •  Question: How Do We Figure Out the Force

on a Point Charge Due to Many Other Point Charges?

•  Answer: Consider One Pair at a Time, Calculate the Force (a Vector!) In Each Case Using Coulomb’s Law and Finally Add All the Vectors! (“Superposition”)

•  Useful To Look Out for SYMMETRY to Simplify Calculations!

Feel the Force! Example

•  Three Equal Charges Form an Equilateral Triangle of Side 1.5 m as Shown

•  Compute the Force on q1

•  ICPP: What are the Forces on the Other Charges?

d

q1

d

d q2

q3

q1= q2= q3= 20 mC d = 1.0 cm

Solution: Set up a Coordinate System, Compute Vector Sum of F12 and F13

d

1

2

3 d

d

12F

13F

o60y

x

Fnet

θ

Feel the Force! Example q1= q2= q3= 20 mC

d = 1.0 cm

d

1

2

3 d

d

12F

13F

o60y

x

Fnet

F12 = F13 =kq1q2

r12( )2

= 8.99 ×109Nm2

C220 ×10−3C 20 ×10−3C

0.01m( )2

=3.60 ×106N

Fnet = Fnetx( )2

+ Fnety( )2

= F13x( )2

+ F13y + F12( )2

= F13 cos(30°)( )2+ F13 sin(30°)+ F12( )2

= 3.12 ×106N( )2+ 5.40 ×106N( )2

= 6.24 ×106N

By geometry: θ = 12 60° + 90° = 120°

θ

ICPP: What are the magnitudes and directions of the forces on 2 and 3?

What is the Force on Central Particle?

Charge +q Placed at Center

Another Example With Symmetry

+q r

All Forces Cancel Except From +2q!

�

! F =

k +2q +qr2

F